Technical Note - EBSD
Triplet Indexing
Introduction
In Orientation Imaging Microscopy (OIM™), indexing is the fundamental process in determining crystallographic orientations
from Electron Backscatter Diffraction (EBSD) patterns. The collected orientation measurements become the “raw” data for all
subsequent processing, making reliable and accurate indexing the pivotal step for a successful analysis. EDAX has experimented
with many indexing methods and found the triplet-voting approach to be the most robust and reliable.
Indexing 101
The bands in an EBSD pattern correspond to crystal lattice
planes within the diffracting volume of the sample. The angles
between the bands correlate to the angles between the planes.
Band widths are related to the spacing between the planes, but
are also affected by the accelerating voltage of the electron
microscope. Taken together, the spatial arrangement of the
bands in a pattern is indicative of the crystal latticeʼs
orientation, relative to the EBSD system geometry.
Hence, the main steps for indexing an EBSD pattern are
to detect the bands, measure them, and then compare the
measurements to known crystal structure data to find the best
fit. Since inter-band angles can be measured more easily and
precisely than band widths, given the relatively low resolution
images common for automated EBSD, angles are typically
preferred over widths for this application. While detecting the
bands and having the correct structural information are critical,
it is finding the best fit between the two that determines the
final solution. For brevity, this review will assume that bands
have been accurately detected and the correct structural data
for the phase is known. The focus is on the actual process used
to derive the most reliable orientation.
It Just Takes Three
The angle between two bands can be compared to a look-up
table of interplanar angles and corresponding Miller Indices,
hklʼs (i.e. the known structural data). Without incorporating
the width data, only an hkl pair can be identified, not which
member of the pair is associated with which band. On the other
hand, if three bands are used, then the indices associated with
each band can be uniquely identified using a logic routine.
Once the indices of the bands are identified, the corresponding
lattice orientation can be determined.
This would seem to imply that a unique orientation solution
could be determined using just one triplet of bands. In practice,
this is generally not the case for the following reasons.
• Band angle measurements have a degree of uncertainty, so
it is necessary to use an angular tolerance or range, to
qualify a match. This, and the variance itself, may result
in more than one possible orientation solution. Figure 2
shows an example of finding two possible matches, given
an angular tolerance of 0.5 degrees.
• False or “rogue” bands could lead to an incorrect solution,
or no solution at all. These bands are quite common in
overlapping patterns, as they are prevalent near grain
boundaries.
Figure 1. Indexing determines a crystal’s orientation information in the EBSD pattern.
Technical Note - EBSD
However, all other orientations determined using combinations
of the remaining six bands will still be valid and the correct
solution can still be found.
The Alternatives: All (or nothing at all)
•
Figure 2. Matching measured angle to reference
structured data.
If one selects a weak, albeit real band from the pattern,
there may not be a match in the look-up table because
weakly reflecting planes are often intentionally excluded
from the reference data to simplify indexing. It should be
noted that these constraints plague all EBSD indexing, not
just the triplet method.
Get Out the Vote
To overcome the difficulties described above, EDAX has
implemented triplet indexing within a novel voting framework.
To begin, all possible combinations of band triplets are
determined from the total number of bands. Then, for each
triplet, the potential orientations are identified, with each
solution getting a vote. When the supply of triplets is
exhausted, the votes are tallied and the orientation with the most
votes among all candidates is selected as the most probable
solution. The voting mechanism opens the door to some very
important benefits.
To the Victor
Voting provides the foundation for EDAXʼs patented
Confidence Index (CI). The CI lets you know when you
can/can not be confident about results by providing a numerical
measure of the indexing solutionʼs accuracy and reliability. The
CI is a very powerful tool and is used extensively throughout
OIM™. It makes it easier to see when something may have
gone wrong, or to determine when and how data might need to
be cleaned up.
The voting method also deals very well with rogue and weak
bands. For example, assume the green band in Figure 3
happens to be from an overlapping pattern. Any solution
involving that band will likely be erroneous.
How does the triplet-voting procedure compare to other
alternatives? For example, what about trying to solve for more
than three bands, en masse? As it turns out, increasing the
number of bands in this manner soon reaches a point of
diminishing returns. Processing additional bands, in an attempt
to get more reliable indexing, is computationally more complex
and takes longer. A more significant problem is that the more
bands one attempts to index at a time, the more difficult it
becomes to find a solution that encompasses and satisfies all of
them. The result is either a higher indexing failure rate or more
zero solutions. This effectively imposes a cap on the number
of bands one can use in practice and clearly creates a trade-off
between speed and accuracy.
In contrast, bringing more bands into the triplet indexing
process simply increases the number of indexing computations,
not the complexity of them. Granted, doubling the number of
bands used would take longer, but the success rate of finding
an index solution is not affected. Because of this, the trade-off
between speed and accuracy is significantly minimized.
Conclusion
Triplet indexing, when combined with a voting strategy,
improves indexing reliability and accuracy and
minimizes trade-off between speed and accuracy. It
also provides a foundation for a numerical measure of
indexing quality, readily handles false bands, and enables
deconvolution of overlapping patterns.
Figure 3. Voting Mechanism.
© EDAX Inc., 2013 November